"It was a difficult game as I predicted it would be," said Swansea manager Paulo Sousa.
"They were well organised but we seemed a little tired and although we created a few good chances we never had any luck.
"The players have plenty of desire and I made the changes at half-time to switch things around and be more aggressive.
"In this type of game we were unable to play the way we would like to but the players are tired both physically and mentally and we haven't had time to prepare for different opponents.
"I have respect for all our opponents and we try to win every game but our fans must be educated to know that they need to help the players and not pass their anxiety on to the field as we need them to believe and support."
Wednesday were desperate for points to pull themselves away from the relegation zone and, after four minutes, Leon Clarke tried to lob home goalkeeper Dorus De Vries only to see the ball land on top of the home netting.
After an ineffective first half, Craig Beattie was replaced by Shefki Kuqi in an effort to unsettle the visiting defence.
Kuqi was immediately in the action, hitting a Cedric van der Gun centre first time just beyond the post with Owls keeper Lee Grant beaten.
Chances were limited at both ends but with Swansea's midfield not operating at their fluent best they were unable to penetrate the visitors' rear guard even with seven minutes of added time.
Wednesday boss Alan Irvine was very pleased with his side's well-earned point.
"I think we deserved a draw and had to work very hard for it as we knew there would be periods when we didn't have the ball and were prepared for that.
"Midway through the first half we began passing the ball much better and it was only in the closing stages that I felt a little worried.
"Swansea have a fantastic record of winning games 1-0 and I was a little nervous as the game moved to a close.
"We have recently played three of the top sides and not looked out of place but we have to build on these performances to push on and have a lot of hard work to do.
"Four games ago we were hammered at Reading but the players have shown great character in coming back from that defeat."